一,Diffusion( P511)
Features:
1,~ What’s diffusion?
Diffusion is the movement,under the influence
of a physical stimulus(物理驱动),of an
individual component(单独的组份)
through a mixture,
8.3.1 Molecular diffusion in binary mixtures
( 扩散和单
向传质)
§ 8.3 Diffusion and mass transfer
within single phase
一,Diffusion( P511)
2,~ Why reason?
The most cause of diffusion is a concentration
gradient of the diffusing component.
3,~ Purpose?
A concentration gradient(浓度梯度) tends to
move the component in such a direction as to equalize
concentration and destroy the gradient.
8.3.1 Molecular diffusion in binary mixtures
( 扩散和单
向传质)
§ 8.3 Diffusion and mass transfer
within single phase
一,Diffusion( P511)
4,~ Steady-state flux
When the gradient is maintained by constantly
supplying the diffusing component to the high-
concentration end of the gradient and removing
it at the low-concentration end,there is a
steady-state flux of the diffusing component,
This is characteristic of many mass-transfer
operations.
8.3.1 Molecular diffusion in binary mixtures
5,~ Other reasons
Although the usual cause of diffusion is a
concentration gradient,diffusion can also be
caused by an activity gradient(能动梯度),
as in reverse osmosis(反渗透),by a
pressure gradient,by a temperature gradient,
or by the application of an external force field
(外场力),as in a centrifuge(离心力场),
8.3.1 Molecular diffusion in binary mixtures
6,What’s thermal diffusion?热扩散
Molecular diffusion induced by temperature
gradient is thermal diffusion.
7,What’s the force diffusion? 强制扩散
Molecular diffusion induced by the
application of a force from an external
filed is forced diffusion.
8.3.1 Molecular diffusion in binary mixtures
8,Diffusion in a direction 扩散方向
Diffusion in a direction is perpendicular
to the interface between the phases and
at a definite location in the equipment.
9,Steady state
Steady state is assumed,and the
concentrations at any point do not
change with time.
8.3.1 Molecular diffusion in binary mixtures
二, Fick’s first law of diffusion for a binary mixture
(P514)(双组份扩散时的费克第一定律)
1,What’s Fick’s first law?
∵ 分子扩散的实质是 分子的微观随机运动 。
∴ 对于一定温度和压力下的一维定态扩散,其统
计规律可用宏观的方式表达。这就是费克定律:
Where,JA= the diffusion flux of component A;
[A moles/per unit area per unit time]
~ [A moles/m2·s]
8.3.1 Molecular diffusion in binary mixtures
? ?AABA dC= - 8 - 9dZJ D
dCA/dz= the concentration gradient of component
A diffusing in a direction,[(mol/m3)/m]
DAB=Diffusivity of component A in
component B,[m2/s ]
Reference to( 8-9),a similar equation for
component B:
∵ For binary mixture DAB=DBA=D
Then JA=- JB ( 8-13)
8.3.1 Molecular diffusion in binary mixtures
? ?BBAB dC= - 8 - 1 1dZJ D
2.,现象定律, ~ That’s phenomena law.
上学期已经学过两个基本定律:
牛顿粘性定律,
~ Newton’s law of viscosity
~ Molecular momentum transport
傅立叶定律,
~ Fourier’s law of heat conduction
~ Molecular energy transport
Comparison to those three formulas:
⑴ 传递的物理量:动量,热量,质量
~ momentum,energy,and mass
8.3.1 Molecular diffusion in binary mixtures
duτμ dy=-
dtq = k dy-
⑵ 均为传递通量, ( 传递的物理量 ) /m2·s
大小 (Magnitudes), 与对应强度因素梯 度成正比。
方向 ( Directions), 沿着浓度减小的方向传递。
⑶ 各式中的系数仅为状态函数,即是 T,P和组成的函
数,而于流动无关。
∴ 又统一称这三个定律为
“现象定律” ~ That’s phenomena law.
∴ 大家在学习质量传递时,完全可以与前面所学过的动
量、热量传递进行类比。
8.3.1 Molecular diffusion in binary mixtures
三,Molecular diffusion and bulk flow
~ 分子扩散与主体流动
1,Molecular diffusion
如图所示:
当挡板被提起后,在浓度
梯度的驱动下,必有 A分子向
右移动,B 分子向左移动 。
8.3.1 Molecular diffusion in binary mixtures
∵ 所讨论的系统均为连续介质
∴ 在容器内 不会产生空位,即有
一个 A分子向右移动,一定会有
一个 B分子向左移动 。
即对于 P-Q plane而言,通过的
净物质为 0,JA=- JB 。
∴ 这种扩散现象称为
等分子反方向扩散
~ Equimolal diffusion.
8.3.1 Molecular diffusion in binary mixtures
8.3.1 Molecular diffusion in binary mixtures
2.One-way diffusion
( one-component mass transfer) ~ 单向扩散
如图,可溶性气体 A通过 气体 B的单向扩散。当 A
被 S吸收时,A→ 扩散,留下空位。
∵ 是连续介质 ∴ 此空位不会被保留,势必由上
方的混合气体来填补。这样便产生了趋于相界面的
,主体流动, 。
Bulk flow~
The convective
bulk flow of the
liquid )。
3.Bulk Flow
Bulk flow is that the molecular symmetric plane
moves to G -- L interface with total fluid flow.
Its driving force is( PA1-PA2),
PA2 is slightly less than PA1.
4.吸收操作中的主体流动
Obviously,there is the bulk flow in gas absorption
operation,Because there is no B in S,S don’t offer B
to gas phase,and the component A is one-way
diffusion in liquid phase.
8.3.1 Molecular diffusion in binary mixtures
四,Diffusion equations
~ 分子扩散的速率方程
由分子扩散和主体流动引起的质量传递速率可通
过总物料衡算和费克定律导出。
由图 8-10,对 PQ平面 To total material balance,
通过 PQ面的净物流 N= NM+ JA+ JB (算术和 )
∵ JA=- JB ∴ N=NM ( 8-14)
Known from 式 (8-14):
⑴ N与 NM的 物理意义不同 (?),但速率 [kmol/s]
相等。 ~相对于静止平面
⑵ For equimolar diffusion,∵ N=0,∴ NM=0
8.3.1 Molecular diffusion in binary mixtures
⑶ Make a material balance for component A:
In general N consists of NA and NB for binary
mixture A+B,that is,N=NA+NB
Then:
~ Molecular diffusion rate equation for component A

∴ ( 8-14)~( 8-16) 均为分子扩散速率微分
式,不能直接使用,需要积分。
8.3.1 Molecular diffusion in binary mixtures
? ?AAMA A A
MM
= + N = + N 8 - 1 5CCN J J
? ? ? ? ABA A A
M
CN = J + N + N 8 - 1 6
C
AB AA dC= - D dZ J
五,Interpretation of diffusion equation of( 8-16)
1.Equation(8-16) is the basic equation for mass-
transfer in a non-turbulent fluid phase.
2.It accounts for the amount of component A carried
by the convective bulk flow of the fluid and the
amount of A being transferred by molecular
diffusion.
3.The vector nature of the fluxes and concentration
gradients must be understood,since these quantities
are characterized by directions and magnitudes.
8.3.1 Molecular diffusion in binary mixtures
4.As derived,the positive sense of the vector is in the
direction of increasing z,which may be either
toward or away from the interface.
5.As shown in Eq(8-16),the sign of the gradient is
opposite to the direction of the diffusion flux,since
diffusion is in the direction of lower
concentration,or,downhill”,like the flow of heat
“down,a temperature gradient.
6.There are several types of situations covered by
Eq(8-16).
8.3.1 Molecular diffusion in binary mixtures
⑴ The simplest case is zero convective flow and
equal-molar counter-diffusion of A and B,as
occurs in the diffusion mixing of two gases,
This is also the case for the diffusion of A and
B in the vapor phase for distillations that have
constant molar overflow.
⑵ The second common case is the diffusion of
only one component of the mixture,where the
convective flow is caused by the diffusion of
that component,
8.3.1 Molecular diffusion in binary mixtures
⑶ Examples include evaporation of a liquid with
diffusion of the vapor from the interface into a gas
stream and condensation of a vapor in the presence
of a no condensable gas.
⑷ Many examples of gas absorption also involve
diffusion of only one component,which creates a
convective flow toward the interface,
7.These two types of mass transfer in gases are treated
in the following section for the simple case of steady-
state mass transfer through a stagnant gas layer or
film of known thickness.
8.3.1 Molecular diffusion in binary mixtures
六,分子扩散速率的积分式
1,Equimolal diffusion
2.Only one way diffusion
At steady-state,NA=constant ~ NA≠ f( z)
1- CA/CM = CB/CM,d CA = - d CB,
NA dz = D CM dCB /CB
8.3.1 Molecular diffusion in binary mixtures
? ? ? ?A A 1 A 2DN = - 8 - 19RT δ pp
? ?
??
??
??
A
A A A B B
M
AA
A
M
C= + + = 0
C
C d C1 - = - D
C d Z
F o r N J N N N
N
,∵

B.C.1,z=0,CB=CB1
B.C.2,z=δ,CB=CB2
8.3.1 Molecular diffusion in binary mixtures
? ?
??
??
??
??
B2
B1
δ
AM
0
M B2
A
B1
B2 B1
BM
B2
B1
M
A A 2 A 1
BM
dC
C M
N dz = D C
dCC
BM
D C C
N = ln
δ C
C - C
C =
C
In
C
CD
Th e n, N = C - C
δ C
( 8 - 20 ) ( 17,16 ):
令,
?
? ?
12
M
1
2
12
M
1
2
T - T
T=
T
ln
T
Δ - Δ
o r Δ T=
Δ
ln
Δ
tt
t
t
组 分 B 的 浓 度 对 数 平 均 值
t h e l o g a r i t h mi c me a n
类 似 于,
3,Analysis Eq,(17-16) ~ (8-20)
a,★ One-way diffusion ~ (See P517 Fig.17.1)
组份 A的浓度分布为~对数曲线
★ Equimolar diffusion
组份 A的浓度分布为~线性
b,One-way diffusion,增加一项 ( CM/CBM)
显然,CM/CBM > 1。
所以,CM/CBM被 称为漂流因子。
8.3.1 Molecular diffusion in binary mixtures
与溶解度系数同理,由于溶液热力学理论发展的不
尽如人意,扩散系数一般也是由实验确定的。如果有的
话,可以直接使用。然而,很多时候是没有的,需要 利
用一定条件下的已知值去求。
D=f( T,P,组成,扩散相, μ)
8.3.2 Diffusivities ~ ( P518~ 522)
gas
phase
不同物质
组成
liquid
phase
in gas phase or
liquid phase
一, Diffusivities的来源
1,By experimental measurements.
2,For common materials,在有关手册中找到。
For example, P365 Appendix 1,~ P366 1.(2)
3.半经验公式
For examples eqs.( 8-23) and( 8-25),
8.3.2 Diffusivities
二, Relationships between diffusivity and
T,P and μ.
For gas phase, Eq.(8-23)
or For liquid phase, Eq,(8-25)
只改变状态参数 T,P,有,
Known,Gas,T↑→D↑↑,P↑→ D↓.
Liquid,T↑→D↑,μ↑→ D↓.
8.3.2 Diffusivities
? ?
? ?
?? ??
?? ????
??
?? ??
?? ??
????
1, 8 1
0
0
0
0
0
0
PT D = D 8 - 2 4
TP
μT D = D 8 - 2 6
T μ
三,组份在 gas phase and liquid phase扩散系数
的比较。
1,From table 8.1 in gas phase,D ~ 10-4 m2/s
From table 8.3 in liquid phase,D~ 10-9 m2/s
相差 5 个数量级。
2.液体中组份浓度对扩散系数有较显著的影响。
CA↑→D↑
一般来说,组分在气、液相的扩散速率
相差约 100倍 。
8.3.2 Diffusivities
一,对流传质浓度分布
1,从流动角度看:
静止流体,u=0 ~ 线性
2,层流( Laminar-flow)
Re较小 ~ 对数曲线
3,湍流( Turbulence)
Re较大,强化了传质过程 ~
二,双膜理论( Film theory) P528
~ 即对流传质的理论模型
尽管,前面已推导到( 8-20)
式。但存在 两个问题,
8.3.3 Mass transfer with convection
? ?MA A 2 A 1
BM
CDN = C - C ( 8 - 2 0 )
δC?
Ques.1:式( 8-20)中的 δ 实际上是一个假想出的
扩散层厚度,它在实际操作中很难准确测定。影响
它的因素很多。
∵ 分子扩散过程是一个随机的无规则运动。
Ques2,只研究了一相内的传质问题。但吸收涉及
到 G~ L两相内 的传质。
∴ 式( 8-20)在实际操作中很难直接使用。
从上世纪 20年代以来,人们一直都是以 L- H
双膜理论来解决 G~ L间的传质问题。
8.3.3 Mass transfer with convection
1.双膜理论的基本论点
⑴在气、液两流体间存在着稳定
的 相界面 。界面两侧各有一个
很薄的有效 滞流膜。 溶质以
分子扩散 方式通过此二膜。
⑵在相界面上,气液两相达到平
衡。
⑶ 膜以外的气液两相中心区,由于两条充分流动,溶质
浓度均匀,全部浓度梯度集中在两个有效膜层内。
8.3.3 Mass transfer with convection
2.在单相内的传质速率方程
∵ 在膜内以分子扩散方式通过
∴ 气相,NA=kG( pG- pi)( 8-28)
液相,NA=kL( Ci- CL)( 8-30)
∵ 为稳定吸收 ∴ ( 8-28)=( 8-30)
NA=kG( pG- pi) = kL( Ci- CL)
3.界面浓度
∵ 根据⑵,在相界面处,气液两相
达到平衡。 ∴ pi=HCi
8.3.3 Mass transfer with convection
气相主体 液相主体
界面浓度,只有一个
独立变量~遵循相
平衡关系